The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in the Homework assignments page will always be accurate.
Wk | Lectures | Sections in Text | Topics |
---|---|---|---|
1 | 6/23 | Presentation of the course | |
6/24 | Chap.2 | Composition laws | |
2 | 6/27 | Chap.3, Chap.4 | Groups |
6/29 | Chap.5 | Subgroups | |
7/01 | Chap.5 | Generators, cyclic groups | |
3 | 7/06 | Chap.6 | Functions |
7/07 | Complements on subgroups, discussion of Quiz 1 (solution) | ||
7/08 | Chap.7 | Bijections | |
4 | 7/11 | Chap.12, Chap.14 | Equivalence relations, homomorphisms |
7/13 | Chap. 15 | Cosets, normal subgroups, quotient groups | |
7/14 | Chap.7 | More on quotients | |
7/15 | Chap.16 | The First Isomorphism Theorem | |
5 | 7/18 | Chap.8 | Symmetric groups (Prof. Tanabe) |
7/20 | Chap. 11 | Cyclic groups and their subgroups - Review session (Prof. Muetzel) | |
7/21 | Midterm Exam | Solution | |
7/22 | Chap. 13 | Lagrange's Theorem and application (S. Chari) | |
6 | 7/25 | More on the order and index of subgroups | |
7/27 | Chap. 8 | The alternating group | |
7/28 | Wrap-up discussion on groups | ||
7/29 | Chap. 17 | Rings | |
7 | 8/01 | Chap. 18 | Morphisms and ideals |
8/03 | Chap. 18 | Properties of ideals | |
8/04 | Discussion on rings | ||
8/05 | Chap. 19 | Quotient rings, fields | |
8 | 8/08 | Chap. 20 | Fields of fractions, complex numbers |
8/10 | Chap. 22, Chap. 24 | Arithmetic in $\mathbb{Z}$ and $F[X]$ | |
8/11 | Complements and discussion on rings | ||
8/12 | Chap. 22, Chap. 25 | Factorization in $\mathbb{Z}$ and $F[X]$ | |
9 | 8/15 | Chap. 26 | Irreducibility in polynomial rings |
8/17 | Chap. 27 | Fields extensions | |
8/18 | Quiz 2 (solution) | ||
8/19 | Chap. 28, Chap. 29 | Degrees of fields extensions | |
10 | 8/22 | Wrap-up | |
8/24 | Chap. 30 | Application: ruler and compass constructions | |
8/29 | Final Examination | due by noon (solution) |